Question

Compute payment schedules for the three loans outlined in Part A. Utilize an online calculator or spreadsheet to determine the loan costs. Subsequently, complete the table below with the following details:

A. Monthly payment based on the term
B. APR (Annual Percentage Rate)
C. Number of payments required

Loan Amount Monthly Payment APR Number of Payments Required
Loan 1
Loan 2
Loan 3

Answer 1

Calculating loan payment schedules involves using formulas for annuities and considering variables such as loan amount, interest rate, and loan term. A 15-year mortgage will have higher monthly payments but lower total interest compared to a 30-year mortgage. Monthly payment can be calculated or estimated using online calculators or spreadsheet formulas.

Step-by-step explanation:

The question involves computing payment schedules for loans, which requires understanding of key financial concepts including monthly payments, APR (Annual Percentage Rate), and the number of payments. These are typically calculated using the formulas for compound interest and payments for annuities.

Loan Payment Calculation

For example, to calculate the monthly payment of a $300,000 loan with a 6% interest rate over 30 years, you would use the formula:

PV = R (1 - (1 + i)^-n) / i

where PV is the present value (loan amount), R is the monthly payment, i is the monthly interest rate (annual interest rate divided by 12), and n is the total number of payments (number of years times 12).

Completing the calculation yields the monthly payment. If making 13 payments a year instead of 12, divide the monthly payment by 12 and add that amount to your regular payment. This method reduces the time and total interest paid on the loan.

Understanding Loan Terms

Mortgage terms of 15 or 30 years affect the amount of interest paid and the monthly payment size. A 15-year mortgage typically has higher monthly payments, but less interest paid over the life of the loan compared to a 30-year mortgage.

Examples of Loan Payment Calculations

To find the monthly payments for the given loans:

• A $200,000 student loan at 6.8% interest over 15 years
• Paying off a $5,000 credit card balance with 21.9% APR by making $300 monthly payments
• A $1,000,000 house loan over 30 years at 6% interest rate

To determine the maximum loan Joanna can afford with $12,000 annual payments at 4.2% interest for 30 years, use the annuity formula to solve for PV.

Answer 2

The question focuses on computing payment schedules for loans using the amortization formula, which combines the present value, interest rate, and the number of payments to calculate monthly payment amounts. Examples demonstrate the use of this formula for different loan scenarios, such as mortgages and credit card debt.

Step-by-step explanation:

The computation of payment schedules for loans typically requires information about the loan amount, the annual percentage rate (APR), and the term or number of payments. To determine the monthly payment on a loan, one of the formulas that can be utilized is the amortization formula, which takes into account the principal amount, the interest rate, and the number of payments to calculate the exact payment amount to be made each period.

In the provided examples, loans with different principals, APRs, and terms are considered. For instance, calculating the monthly payment of a $300,000 loan with a 6% interest rate over 30 years involves using this formula in conjunction with an online calculator or a spreadsheet. The formula below represents how to find the periodic payment (R) when the present value (PV), interest rate per period (i), and the number of periods (n) are known:

Applying the formula requires converting the APR to a monthly interest rate and identifying the total number of payments. For example, a 6% interest rate annually translates to a monthly rate of 0.5% when divided by 12. If making 13 payments a year, this would effectively shorten the loan term and save on total interest paid.

To address the examples given, the monthly payments on a $5,000 credit card debt with 24.99% APR paid off over 3 years or the monthly payment for a $270,000 house loan at a 3% interest rate over 30 years can be found by plugging the respective values into the above formula or using an online mortgage calculator tool.

Lastly, it is worth noting that for a $1,000,000 loan at 6% over 30 years, the monthly payment will be $5,995.51, resulting in a total repayment of over $2.1 million, exemplifying the significance of understanding loan terms and ensuring they are affordable before committing to such financial obligations.